1. Field of the Invention
This invention relates to a circuit layout configuration, for example, a circuit layout configuration to improve matching characteristics of a transistor pair in a circuit having the transistor pair such as a current mirror circuit and a differential amplifier.
2. Description of the Related Art
Close matching between the transistors is important for the configuration of the current mirror circuit and of the differential amplifier. In particular, the close matching helps in obtaining a low offset operational amplifier. FIG. 7 is a circuit diagram showing a differential gain stage. A pair of MOS transistors M3 and M4 forms a current mirror circuit 10 and another pair of MOS transistors M1 and M2 forms a differential input pair 11. Each of the pairs of MOS transistors requires close matching respectively.
The most basic layout scheme to implement the current mirror circuit 10 is a lateral layout scheme. A better option is a common-centroid layout scheme. These layout schemes and a scheme called four-segment layout scheme are described in the following document.
Mao-Feng Lan, Anilkumar Tammineedi and Randall Geiger, “Current Mirror Layout Strategies for Enhancing Matching Performance”, Analog Integrated Circuits and Signal Processing, vol. 28, PP. 9-26, July 2001.
These conventional layout schemes will be explained hereinafter. FIG. 8 shows the common-centroid layout scheme. FIG. 9 shows an equivalent circuit of FIG. 8. M1 and M2 are MOS field effect transistors that are to be matched. The transistor M1 is divided into two sub-transistors MS11 and MS12. Similarly, the transistor M2 is divided into two sub-transistors MS21 and MS22.
Since these sub-transistors have a common center P as shown in FIG. 8, it is called the common-centroid layout scheme. And gates, drains and sources of the sub-transistors MS11 and MS12 are connected in common to form the transistor M1, as shown in FIG. 9. Similarly, gates, drains and sources of the sub-transistors MS21 and MS22 are connected in common to form the transistor M2.
And now, when the following document on transistor-matching and process-dependent layout structures is referred, transistors in various layouts are modeled.
M. J. M. Pelgrom, A. C. J. Duinmaijer and A. P. G. Welbers, “Matching properties of MOS transistors” IEEE JSSC, Vol. SC-24, PP. 1433-1439, 1989.
According to the document, an equivalent threshold voltage for such a device is given by the following equation.
      V    Teq    =                    ∫        active            ⁢                        ∫          area                ⁢                                            V              T                        ⁡                          (                              x                ,                y                            )                                ⁢                                          ⁢                      ⅆ            x                    ⁢                                          ⁢                      ⅆ            y                                ActiveArea  
Here, the Active Area denotes an active area of the sub-transistor, that is, a channel region through which a current flows. VT(x, y) is a local threshold voltage that depends on x and y coordinates. A surface integral of VT(x, y) over the active region is calculated to find its average.
And the threshold voltage varies from place to place on a surface of a wafer because of processing. Modeling of the variation in the threshold voltage is made possible by introducing a gradient amplitude a and a gradient direction θ from an origin O shown in FIG. 8.
Therefore, each of corresponding threshold voltages VT11, VT12, VT21 and VT22 can be obtained by applying such a threshold voltage model to each of the above mentioned sub-transistors MS11, MS12, MS21 and MS22, respectively.
First, the threshold voltage VT11 of the sub-transistor MS11 is given by the following equation.
            MS11      ⁢              :              ⁢                            V      T11        =                            ∫                      (                                          L                S                            +                              d                2                                      )                                (                                          2                ⁢                                  L                  S                                            +                              d                2                                      )                          ⁢                              ∫                          (                                                W                  S                                +                                  d                  1                                            )                                      (                                                2                  ⁢                                      W                    S                                                  +                                  d                  1                                            )                                ⁢                                    [                                                                                                                  V                        T                                            +                                              (                                                                              L                            S                                                    ⁢                          αsinθ                                                )                                            +                                                                                                                                  (                                                                        W                          S                                                ⁢                        αcosθ                                            )                                                                                  ]                        ×                          [                                                          ⁢                              ⅆ                W                            ]                        ×                          [                                                          ⁢                              ⅆ                L                            ]                                                            W          s                ×                  L          S                                V      T11        =                            ∫                      (                                          L                S                            +                              d                2                                      )                                (                                          2                ⁢                                  L                  S                                            +                              d                2                                      )                          ⁢                              [                                                                                                                              V                        T                                            ⁢                                              W                        S                                                              +                                                                  L                        S                                            ⁢                                              W                        S                                            ⁢                      αsinθ                                        +                    αcosθ                                                                                                                    (                                                                                                                                            ⁢                                                                                                            (                                                                                                d                                  1                                                                +                                                                  2                                  ⁢                                                                      W                                    S                                                                                                                              )                                                        2                                                    -                                                                                    (                                                                                                d                                  1                                                                +                                                                  W                                  S                                                                                            )                                                        2                                                                                              2                                        )                                                                        ]                    ⁡                      [                          ⅆ              L                        ]                                                W          s                ×                  L          S                                V      T11        =                            ∫                      (                                          L                S                            +                              d                2                                      )                                (                                          2                ⁢                                  L                  S                                            +                              d                2                                      )                          ⁢                              [                                                                                                                              V                        T                                            ⁢                                              W                        S                                                              +                                                                  L                        S                                            ⁢                                              W                        S                                            ⁢                      αsinθ                                        +                                                                                                                    αcosθ                    (                                                                                                                                            ⁢                                                                                                                                                                              d                                  1                                  2                                                                +                                                                  4                                  ⁢                                                                      W                                    S                                    2                                                                                                  +                                                                  4                                  ⁢                                                                      d                                    1                                                                    ⁢                                                                      W                                    S                                                                                                  -                                                                                                                                                                                                                                          d                                  1                                  2                                                                -                                                                  W                                  S                                  2                                                                -                                                                  2                                  ⁢                                                                      d                                    1                                                                    ⁢                                                                      W                                    S                                                                                                                                                                                                                          2                                        )                                                                        ]                    ⁡                      [                          ⅆ              L                        ]                                                W          s                ×                  L          S                                V      T11        =                            ∫                      (                                          L                S                            +                              d                2                                      )                                (                                          2                ⁢                                  L                  S                                            +                              d                2                                      )                          ⁢                              [                                                                                                                              V                        T                                            ⁢                                              W                        S                                                              +                                                                  L                        S                                            ⁢                                              W                        S                                            ⁢                      αsinθ                                        +                    αcosθ                                                                                                                    (                                                                                                                                            ⁢                                                                              3                            ⁢                                                          W                              S                              2                                                                                +                                                      2                            ⁢                                                          W                              S                                                        ⁢                                                          d                              1                                                                                                                          2                                        )                                                                        ]                    ⁡                      [                          ⅆ              L                        ]                                                W          S                ×                  L          S                                V      T11        =                            ∫                      (                                          L                S                            +                              d                2                                      )                                (                                          2                ⁢                                  L                  S                                            +                              d                2                                      )                          ⁢                              [                                                                                                      V                      T                                        +                                                                  L                        S                                            ⁢                      αsinθ                                        +                                                                                                                    αcosθ                    ⁡                                          (                                                                                                                                                                                          ⁢                                                          3                              ⁢                                                              W                                S                                                                                                              2                                                +                                                  d                          1                                                                    )                                                                                            ]                    ⁡                      [                          ⅆ              L                        ]                                      L        S                        V      T11        =                                                      [                                                                    V                    T                                    ⁢                                      L                    S                                                  +                                  αcosθ                  ⁢                                                                          ⁢                                      (                                                                                                                                                                            ⁢                                                      3                            ⁢                                                          W                              S                                                                                                      2                                            +                                              d                        1                                                              )                                    ⁢                                                                          ⁢                                      L                    S                                                  +                                                                                                        αsinθ                ⁢                                                                  ⁢                                  (                                                                                                              (                                                                                    2                              ⁢                                                              L                                S                                                                                      +                                                          d                              2                                                                                )                                                2                                            -                                                                        (                                                                                    L                              S                                                        +                                                          d                              2                                                                                )                                                2                                                              2                                    )                                            ]                                                  L        S                        V      T11        =                  [                                                                                                  V                    T                                    ⁢                                      L                    S                                                  +                                  αcosθ                  ⁢                                                                          ⁢                                      (                                                                                                                                                                            ⁢                                                      3                            ⁢                                                          W                              S                                                                                                      2                                            +                                              d                        1                                                              )                                    ⁢                                                                          ⁢                                      L                    S                                                  +                                                                                        αsinθ                ⁡                                  (                                                                                    4                        ⁢                                                  L                          S                          2                                                                    +                                              d                        2                        2                                            +                                              4                        ⁢                                                  L                          S                                                ⁢                                                  d                          2                                                                    -                                              L                        S                        2                                            -                                              d                        2                        2                                            -                                              2                        ⁢                                                  L                          S                                                ⁢                                                  d                          2                                                                                      2                                    )                                                                    ]                    L        S                                                      V            T11                    =                                    [                                                                    V                    T                                    ⁢                                      L                    S                                                  +                                  αcosθ                  ⁢                                                                          ⁢                                      (                                                                                                                                                                            ⁢                                                      3                            ⁢                                                          W                              S                                                                                                      2                                            +                                              d                        1                                                              )                                    ⁢                                                                          ⁢                                      L                    S                                                  +                                  αsinθ                  ⁢                                                                          ⁢                                      (                                                                                            3                          ⁢                                                      L                            S                            2                                                                          +                                                  2                          ⁢                                                      L                            S                                                    ⁢                                                      d                            2                                                                                              2                                        )                                                              ]                                      L              S                                                                                V            T11                    =                                    V              T                        +                          α              ⁢                                                          ⁢                              (                                                                                                                                                ⁢                                              3                        ⁢                                                  W                          S                                                                                      2                                    +                                      d                    1                                                  )                            ⁢                                                          ⁢              cos              ⁢                                                          ⁢              θ                        +                          α              ⁢                                                          ⁢                              (                                                                            3                      ⁢                                              L                        S                                                              2                                    +                                      d                    2                                                  )                            ⁢                                                          ⁢              sin              ⁢                                                          ⁢              θ                                          
Similarly, the threshold voltage VT12 of the sub-transistor MS12 is given by the following equation.
      MS12    ⁢          :        ⁢                  ⁢          V      T12        =            V      T        +                            W          S                2            ⁢      αcosθ        +                            L          S                2            ⁢      αsinθ      
Similarly, the threshold voltage VT21 of the sub-transistor MS21 is given by the following equation.
      MS21    ⁢          :        ⁢                  ⁢          V      T21        =            V      T        +          α      ⁢                          ⁢              (                                            3              ⁢                              W                S                                      2                    +                      d            1                          )            ⁢                          ⁢      cos      ⁢                          ⁢      θ        +                            L          S                2            ⁢      αsinθ      
Similarly, the threshold voltage VT22 of the sub-transistor MS22 is given by the following equation.
      MS22    ⁢          :        ⁢                  ⁢          V      T22        =            V      T        +                            W          S                2            ⁢      αcosθ        +          α      ⁢                          ⁢              (                                            3              ⁢                              L                S                                      2                    +                      d            2                          )            ⁢                          ⁢      sin      ⁢                          ⁢      θ      
In the equations described above, d1 denotes a distance between drains (sources) of neighboring sub-transistors, d2 denotes a distance between gates of neighboring sub-transistors, Ws denotes a width of the gate of the sub-transistor and Ls denotes a length of the gate of the sub-transistor.
Next, FIG. 10 shows the four-segment layout scheme. FIG. 11 shows an equivalent circuit of FIG. 10. M1 and M2 are MOS field effect transistors that are to be matched. The transistor M1 is divided into four sub-transistors MS11, MS12, MS13 and MS14. These sub-transistors are disposed in four segments.
Similarly, the transistor M2 is divided into four sub-transistors MS21, MS22, MS23 and MS24. These sub-transistors are disposed in four segments.
An origin O, a gradient amplitude a and a gradient direction θ are also defined with respect to the four-segment layout scheme as shown in FIG. 10, and equations below that describe results of the modeling of the threshold values are obtained. That is, it is assumed in the following equations that a threshold value of the sub-transistor MS11 is VT11, a threshold value of the sub-transistor MS12 is VT12, a threshold value of the sub-transistor MS13 is VT13, a threshold value of the sub-transistor MS14 is VT14, a threshold value of the sub-transistor MS21 is VT21, a threshold value of the sub-transistor MS22 is VT22, a threshold value of the sub-transistor MS23 is VT23 and a threshold value of the sub-transistor MS24 is VT24.
            MS11      ⁢              :            ⁢                          ⁢              V        T11              =                  V        T            -                        α          ⁡                      (                                          W                2                            +                                                d                  1                                2                                      )                          ⁢                                  ⁢        cos        ⁢                                  ⁢        θ            +              α        ⁢                                  ⁢                  (                                    L              2                        +            W            +                                          3                ⁢                                  d                  1                                            2                                )                ⁢                                  ⁢        sin        ⁢                                  ⁢        θ                        MS12      ⁢              :            ⁢                          ⁢              V        T12              =                  V        T            +                        α          ⁡                      (                          W              +                              L                2                            +                                                3                  ⁢                                      d                    1                                                  2                                      )                          ⁢                                  ⁢        cos        ⁢                                  ⁢        θ            +              α        ⁢                                  ⁢                  (                                    W              2                        +                                          d                1                            2                                )                ⁢                                  ⁢        sin        ⁢                                  ⁢        θ                        MS13      ⁢              :            ⁢                          ⁢              V        T13              =                  V        T            +                        α          ⁡                      (                                          W                2                            +                                                d                  1                                2                                      )                          ⁢                                  ⁢        cos        ⁢                                  ⁢        θ            -              α        ⁢                                  ⁢                  (                                    L              2                        +            W            +                                          3                ⁢                                  d                  1                                            2                                )                ⁢                                  ⁢        sin        ⁢                                  ⁢        θ                        MS14      ⁢              :            ⁢                          ⁢              V        T14              =                  V        T            -                        α          ⁡                      (                          W              +                              L                2                            +                                                3                  ⁢                                      d                    1                                                  2                                      )                          ⁢                                  ⁢        cos        ⁢                                  ⁢        θ            -              α        ⁢                                  ⁢                  (                                    W              2                        +                                          d                1                            2                                )                ⁢                                  ⁢        sin        ⁢                                  ⁢        θ                        MS21      ⁢              :            ⁢                          ⁢              V        T21              =                  V        T            +                        α          ⁡                      (                                          W                2                            +                                                d                  1                                2                                      )                          ⁢                                  ⁢        cos        ⁢                                  ⁢        θ            +              α        ⁢                                  ⁢                  (                                    L              2                        +            W            +                                          3                ⁢                                  d                  1                                            2                                )                ⁢                                  ⁢        sin        ⁢                                  ⁢        θ                        MS22      ⁢              :            ⁢                          ⁢              V        T22              =                  V        T            +                        α          ⁡                      (                          W              +                              L                2                            +                                                3                  ⁢                                      d                    1                                                  2                                      )                          ⁢                                  ⁢        cos        ⁢                                  ⁢        θ            -              α        ⁢                                  ⁢                  (                                    W              2                        +                                          d                1                            2                                )                ⁢                                  ⁢        sin        ⁢                                  ⁢        θ                        MS23      ⁢              :            ⁢                          ⁢              V        T23              =                  V        T            -                        α          ⁡                      (                                          W                2                            +                                                d                  1                                2                                      )                          ⁢                                  ⁢        cos        ⁢                                  ⁢        θ            -              α        ⁢                                  ⁢                  (                                    L              2                        +            W            +                                          3                ⁢                                  d                  1                                            2                                )                ⁢                                  ⁢        sin        ⁢                                  ⁢        θ                        MS24      ⁢              :            ⁢                          ⁢              V        T24              =                  V        T            -                        α          ⁡                      (                          W              +                              L                2                            +                                                3                  ⁢                                      d                    1                                                  2                                      )                          ⁢                                  ⁢        cos        ⁢                                  ⁢        θ            +              α        ⁢                                  ⁢                  (                                    W              2                        +                                          d                1                            2                                )                ⁢                                  ⁢        sin        ⁢                                  ⁢        θ            
In the equations described above, d1 denotes a distance between drains (sources) of neighboring sub-transistors, Ws denotes a width of a gate of the sub-transistor and Ls denotes a length of the gate of the sub-transistor.